The discussion focuses on using the limit definition to find the derivative of the function f(x) = x^2 - 4x. The derivative is defined as the limit of the ratio [f(x+h) - f(x)]/h as h approaches 0. The calculation involves substituting f(x+h) into the limit definition, leading to the expression 2hx + h^2 - 4h. This method is essential for understanding the foundational concepts of calculus as outlined in Larson's "Precalculus: Graphing with Limits".
PREREQUISITESStudents learning calculus, educators teaching derivative concepts, and anyone seeking to strengthen their understanding of limit definitions in mathematics.
I don't have the Larson book, but I assume it defines the derivative (not _derivation_) of f at x to be the limit of the ratio [f(x+h) - f(x)]/h as h --> 0. Well, you can calculate f(x+h) and you know f(x), so you can see what the ratio is equal to. Then you can see what it becomes closer and closer to as h becomes smaller and smaller.epatjn said:Homework Statement
Here's the question...use the limit definition to find the derivation of f(x) = x^2-4x
Homework Equations
does this use the definition of the derivative formula (using Larson, et al 4th edition of Precaclulus graphing with limits...and trying to teach someone what to do, but am at a loss at present on what to do...
The Attempt at a Solution